Regression with n$\to$1 by Expert Knowledge Elicitation

TL;DR

This paper addresses regression in extremely small sample size scenarios by leveraging expert knowledge to improve prediction accuracy, especially in high-dimensional genomics data, through an optimal elicitation strategy.

Contribution

It introduces a novel framework for incorporating expert feedback into regression with very limited data, including an elicitation strategy and optimality conditions.

Findings

Elicitation strategy significantly improves prediction accuracy.

Proposed method effective in synthetic and genomics data.

Strategy is optimal under certain conditions.

Abstract

We consider regression under the "extremely small $n$ large $p$" condition, where the number of samples $n$ is so small compared to the dimensionality $p$ that predictors cannot be estimated without prior knowledge. This setup occurs in personalized medicine, for instance, when predicting treatment outcomes for an individual patient based on noisy high-dimensional genomics data. A remaining source of information is expert knowledge, which has received relatively little attention in recent years. We formulate the inference problem of asking expert feedback on features on a budget, propose an elicitation strategy for a simple "small $n$" setting, and derive conditions under which the elicitation strategy is optimal. Experiments on simulated experts, both on synthetic and genomics data, demonstrate that the proposed strategy can drastically improve prediction accuracy.